1,761 research outputs found
Some branching formulas for Kac--Moody Lie algebras
In this paper we give some branching rules for the fundamental
representations of Kac--Moody Lie algebras associated to -shaped graphs.
These formulas are useful to describe generators of the generic rings for free
resolutions of length three described in [JWm16]. We also make some conjectures
about the generic rings
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
A combinatorial description of the crystal B(infinity) for finite-dimensional
simple Lie algebras in terms of certain Young tableaux was developed by J. Hong
and H. Lee. We establish an explicit bijection between these Young tableaux and
canonical bases indexed by Lusztig's parametrization, and obtain a
combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum
over the set of Young tableaux.Comment: 19 page
Vertex Operator Algebras Associated to Type G Affine Lie Algebras
In this paper, we study representations of the vertex operator algebra
at one-third admissible levels for the affine
algebra of type . We first determine singular vectors and then
obtain a description of the associative algebra using the singular
vectors. We then prove that there are only finitely many irreducible
-modules from the category . Applying the -theory,
we prove that there are only finitely many irreducible weak -modules
from the category and that such an -module is completely
reducible. Our result supports the conjecture made by Adamovi{\'c} and Milas in
\cite{AM}.Comment: 30 page
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